標題: Noncircular elliptic discs as numerical ranges of nilpotent operators
作者: Gau, Hwa-Long
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: numerical range;nilpotent operator;quasinilpotent operator;essential numerical range
公開日期: 2012
摘要: We show that (1) if A is a nonzero quasinilpotent operator with ran A(n) closed for some n >= 1, then its numerical range W(A) contains 0 in its interior and has a differentiable boundary, and (2) a noncircular elliptic disc can be the numerical range of a nilpotent operator with nilpotency 3 on an infinite-dimensional separable space. (1) is a generalization of the known result for nonzero nilpotent operators, and (2) is in contrast to the finite-dimensional case, where the only elliptic discs which are the numerical ranges of nilpotent finite matrices are the circular ones centred at the origin.
URI: http://hdl.handle.net/11536/20509
http://dx.doi.org/10.1080/03081087.2011.611945
ISSN: 0308-1087
DOI: 10.1080/03081087.2011.611945
期刊: LINEAR & MULTILINEAR ALGEBRA
Volume: 60
Issue: 11-12
起始頁: 1225
結束頁: 1233
Appears in Collections:Articles


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